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   "source": [
    "<center><strong>中文自然语言处理</strong></center>\n",
    "<center><strong>Transformer模型(二)</strong></center>\n",
    "<center><strong>BERT的预训练与应用</strong></center>"
   ]
  },
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   "metadata": {},
   "source": [
    "__二. transformer代码解读, 语料数据预处理, BERT的预训练和情感分析的应用__:\n",
    "1. 结合注意力矩阵可视化位置编码;\n",
    "2. 语言模型的定义和BERT解读;\n",
    "3. BERT训练之前的准备工作, 语料预处理;\n",
    "4. BERT预训练;\n",
    "5. 使用BERT预训练模型进行自然语言的情感分类."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "        <script type=\"text/javascript\">\n",
       "        window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
       "        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
       "        if (typeof require !== 'undefined') {\n",
       "        require.undef(\"plotly\");\n",
       "        requirejs.config({\n",
       "            paths: {\n",
       "                'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
       "            }\n",
       "        });\n",
       "        require(['plotly'], function(Plotly) {\n",
       "            window._Plotly = Plotly;\n",
       "        });\n",
       "        }\n",
       "        </script>\n",
       "        "
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 导入依赖库\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import math\n",
    "import plotly.graph_objs as go\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
    "from IPython.display import Image \n",
    "init_notebook_mode(connected=True)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_positional_encoding(max_seq_len, embed_dim):\n",
    "    # 初始化一个positional encoding\n",
    "    # embed_dim: 字嵌入的维度\n",
    "    # max_seq_len: 最大的序列长度\n",
    "    positional_encoding = np.array([\n",
    "        [pos / np.power(10000, 2 * i / embed_dim) for i in range(embed_dim)]\n",
    "        if pos != 0 else np.zeros(embed_dim) for pos in range(max_seq_len)])\n",
    "    positional_encoding[1:, 0::2] = np.sin(positional_encoding[1:, 0::2])  # dim 2i 偶数\n",
    "    positional_encoding[1:, 1::2] = np.cos(positional_encoding[1:, 1::2])  # dim 2i+1 奇数\n",
    "    # 归一化, 用位置嵌入的每一行除以它的模长\n",
    "    # denominator = np.sqrt(np.sum(position_enc**2, axis=1, keepdims=True))\n",
    "    # position_enc = position_enc / (denominator + 1e-8)\n",
    "    return positional_encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "positional_encoding = get_positional_encoding(max_seq_len=100, embed_dim=128)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
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   ],
   "source": [
    "# 3d可视化\n",
    "relation_matrix = np.dot(positional_encoding, positional_encoding.T)[1:, 1:]\n",
    "data = [go.Surface(z=relation_matrix)]\n",
    "layout = go.Layout()\n",
    "fig = go.Figure(data=data, layout=layout)\n",
    "iplot(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. 语言模型的定义和BERT解读;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "什么是语言模型, 其实用一个公式就可以表示$P(c_{1},\\ldots ,c_{m})$, 假设我们有一句话, $c_{1}到c_{m}$是这句话里的$m$个字, 而语言模型就是求的是这句话出现的概率是多少.   \n",
    "\n",
    "比如说在一个语音识别的场景, 机器听到一句话是\"wo wang dai san le(我忘带伞了)\", 然后机器解析出两个句子, 一个是\"我网袋散了\", 另一个是\"我忘带伞了\", 也就是前者的概率大于后者. 然后语言模型就可以判断$P(\"我忘带伞了\") > P(\"我网袋散了\")$, 从而得出这句语音的正确解析结果是\"我忘带伞了\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "BERT的全称是: Bidirectional Encoder Representations from Transformers, 如果翻译过来也就是**双向transformer编码表达**, 我们在上节课解读了transformer的编码器, 编码器输出的隐藏层就是自然语言序列的数学表达, 那么双向是什么意思呢? 我们来看一下下面这张图."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](./imgs/bidirectional.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上图中$E_i$是指的单个字或词, $T_i$指的是最终计算得出的**隐藏层**, 还记得我们在Transformer(一)中讲到的注意力矩阵和注意力加权, 经过这样的操作之后, 序列里面的每一个字, **都含有这个字前面的信息和后面的信息**, 这就是**双向**的理解, 在这里, 一句话中每一个字, 经过注意力机制和加权之后, **当前这个字等于用这句话中其他所有字重新表达了一遍**, 每个字含有了这句话中所有成分的信息.\n",
    "\n",
    "#### 在BERT中, 主要是以两种预训练的方式来建立语言模型:\n",
    "#### BERT语言模型任务一: MASKED LM\n",
    "在BERT中, Masked LM(Masked language Model)构建了语言模型, 这也是BERT的预训练中任务之一, 简单来说, 就是**随机遮盖或替换**一句话里面任意字或词, 然后让模型通过上下文的理解预测那一个被遮盖或替换的部分, 之后**做$Loss$的时候只计算被遮盖部分的$Loss$**, 其实是一个很容易理解的任务, 实际操作方式如下:   \n",
    "1. 随机把一句话中$15 \\% $的$token$替换成以下内容:   \n",
    "1) 这些$token$有$80 \\% $的几率被替换成$[mask]$;   \n",
    "2) 有$10 \\%$的几率被替换成任意一个其他的$token$;   \n",
    "3) 有$10 \\%$的几率原封不动.\n",
    "2. 之后让模型**预测和还原**被遮盖掉或替换掉的部分, 模型最终输出的隐藏层的计算结果的维度是:   \n",
    "$X_{hidden}: [batch\\_size, \\ seq\\_len, \\  embedding\\_dim]$   \n",
    "我们初始化一个映射层的权重$W_{vocab}$:   \n",
    "$W_{vocab}: [embedding\\_dim, \\ vocab\\_size]$   \n",
    "我们用$W_{vocab}$完成隐藏维度到字向量数量的映射, 只要求$X_{hidden}$和$W_{vocab}$的矩阵乘(点积):   \n",
    "$X_{hidden}W_{vocab}: [batch\\_size, \\ seq\\_len, \\ vocab\\_size] $\n",
    "之后把上面的计算结果在$vocab\\_size$(最后一个)维度做$softmax$归一化, 是每个字对应的$vocab\\_size$的和为$1$, 我们就可以通过$vocab\\_size$里概率最大的字来得到模型的预测结果, 就可以和我们准备好的$Label$做损失($Loss$)并反传梯度了.   \n",
    "注意做损失的时候, 只计算在第1步里当句中**随机遮盖或替换**的部分, 其余部分不做损失, 对于其他部分, 模型输出什么东西, 我们不在意."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BERT语言模型任务二: Next Sentence Prediction\n",
    "1. 首先我们拿到属于上下文的一对句子, 也就是两个句子, 之后我们要在这两段连续的句子里面加一些特殊$token$:   \n",
    "$[cls]$上一句话,$[sep]$下一句话.$[sep]$   \n",
    "也就是在句子开头加一个$[cls]$, 在两句话之中和句末加$[sep]$, 具体地就像下图一样:   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](./imgs/embeddings.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. 我们看到上图中两句话是$[cls]$ my dog is cute $[sep]$ he likes playing $[sep]$, $[cls]$我的狗很可爱$[sep]$他喜欢玩耍$[sep]$, 除此之外, 我们还要准备同样格式的两句话, 但他们不属于上下文关系的情况;   \n",
    "$[cls]$我的狗很可爱$[sep]$企鹅不擅长飞行$[sep]$, 可见这属于上下句不属于上下文关系的情况;    \n",
    "在实际的训练中, 我们让上面两种情况出现的比例为$1:1$, 也就是一半的时间输出的文本属于上下文关系, 一半时间不是.\n",
    "3. 我们进行完上述步骤之后, 还要随机初始化一个可训练的$segment \\ embeddings$, 见上图中, 作用就是用$embeddings$的信息让模型分开上下句, 我们一把给上句全$0$的$token$, 下句啊全$1$的$token$, 让模型得以判断上下句的起止位置, 例如:   \n",
    "$[cls]$我的狗很可爱$[sep]$企鹅不擅长飞行$[sep]$   \n",
    "$0 \\quad  \\  0 \\ \\ 0 \\ \\  0 \\ \\ 0 \\ \\ 0 \\ \\ 0 \\ \\  0 \\ \\ \\ 1 \\ \\  1 \\ \\ 1 \\ \\ 1 \\ \\ 1 \\ \\ 1 \\ \\ 1 \\ \\ 1 $    \n",
    "上面$0$和$1$就是$segment \\ embeddings$.\n",
    "4. 还记得我们上节课说过的, 注意力机制就是, 让每句话中的每一个字对应的那一条向量里, 都融入这句话所有字的信息, 那么我们在最终隐藏层的计算结果里, 只要取出$[cls]token$所对应的一条向量, 里面就含有整个句子的信息, 因为我们期望这个句子里面所有信息都会往$[cls]token$所对应的一条向量里汇总:   \n",
    "模型最终输出的隐藏层的计算结果的维度是:   \n",
    "我们$X_{hidden}: [batch\\_size, \\ seq\\_len, \\  embedding\\_dim]$   \n",
    "我们要取出$[cls]token$所对应的一条向量, $[cls]$对应着$\\ seq\\_len$维度的第$0$条:   \n",
    "$cls\\_vector = X_{hidden}[:, \\ 0, \\ :]$   \n",
    "$cls\\_vector \\in \\mathbb{R}^{batch\\_size, \\  embedding\\_dim}$   \n",
    "之后我们再初始化一个权重, 完成从$embedding\\_dim$维度到$1$的映射, 也就是逻辑回归, 之后用$sigmoid$函数激活, 就得到了而分类问题的推断.\n",
    "\n",
    "至此$BERT$的训练的内容就讲完了"
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